What is (1-3/4)(3-2 1/2) ?

The solution to (1-3/4)(3-2 1/2) is 1/8

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(1-3/4)(3-2 1/2)

(1 - \frac{3}{4}) (3 - 2 \frac{1}{2})

\frac{1}{8}

Solution steps

(1 - \frac{3}{4}) (3 - 2 \frac{1}{2})

Convert mixed numbers to improper fractions:

2 \frac{1}{2} = \frac{5}{2}

2 \frac{1}{2}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

2 \frac{1}{2} = \frac{2 \cdot 2 + 1}{2}

= \frac{5}{2}

= (1 - \frac{3}{4}) (3 - \frac{5}{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - \frac{3}{4}) : \frac{1}{4}

1 - \frac{3}{4}

1 - \frac{3}{4} = \frac{1}{4}

1 - \frac{3}{4}

Convert element to fraction:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{3}{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 4 - 3}{4}

1 \cdot 4 - 3 = 1

1 \cdot 4 - 3

Multiply the numbers:

1 \cdot 4 = 4

= 4 - 3

Subtract the numbers:

4 - 3 = 1

= 1

= \frac{1}{4}

= \frac{1}{4}

= \frac{1}{4} (3 - \frac{5}{2})

Calculate within parentheses

(3 - \frac{5}{2}) : \frac{1}{2}

3 - \frac{5}{2}

3 - \frac{5}{2} = \frac{1}{2}

3 - \frac{5}{2}

Convert element to fraction:

3 = \frac{3 \cdot 2}{2}

= \frac{3 \cdot 2}{2} - \frac{5}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 \cdot 2 - 5}{2}

3 \cdot 2 - 5 = 1

3 \cdot 2 - 5

Multiply the numbers:

3 \cdot 2 = 6

= 6 - 5

Subtract the numbers:

6 - 5 = 1

= 1

= \frac{1}{2}

= \frac{1}{2}

= \frac{1}{4} \cdot \frac{1}{2}

Multiply and divide (left to right)

\frac{1}{4} \cdot \frac{1}{2} : \frac{1}{8}

\frac{1}{4} \cdot \frac{1}{2}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{4 \cdot 2}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{1}{8}

= \frac{1}{8}

15 \div 3 + 2 + 20 \div (2 + 2)

2 (6)^{2}

2^{2} \times 2

2 (2) - 4

(0)^{2} - 2 (0)